The surging popularity of adopting industrial robots in smart manufacturing has led to an increasing trend in the simultaneous improvement of the energy costs and operational efficiency of motion trajectory. Motivated by this, multi-objective trajectory planning subject to kinematic and dynamic constraints at multiple levels has been considered as a promising paradigm to achieve the improvement. However, most existing model-based multi-objective optimization algorithms tend to come out with infeasible solutions, which results in non-zero initial and final acceleration. Popular commercial software toolkits applied to solve multi-objective optimization problems in actual situations are mostly based on the fussy conversion of the original objective and constraints into strict convex functions or linear functions, which could induce a failure of duality and obtain results exceeding limits. To address the problem, this paper proposes a time-energy optimization model in a phase plane based on the Riemann approximation method and a solution scheme using an iterative learning algorithm with neural networks. We present forward-substitution interpolation functions as basic functions to calculate indirect kinematic and dynamic expressions introduced in a discrete optimization model with coupled constraints. Moreover, we develop a solution scheme of the complex trajectory optimization problem based on artificial neural networks to generate candidate solutions for each iteration without any conversion into a strict convex function, until minimum optimization objectives are achieved. Experiments were carried out to verify the effectiveness of the proposed optimization solution scheme by comparing it with state-of-the-art trajectory optimization methods using Yalmip software. The proposed method was observed to improve the acceleration control performance of the solved robot trajectory by reducing accelerations exceeding values of joints 2, 3 and 5 by 3.277 rad/s², 26.674 rad/s², and 7.620 rad/s², respectively.

This paper aims to address the issue of explicitly utilizing the joint limit avoidance, singularity avoidance, and self-motion obstacle avoidance properties of a 7-degrees-of-freedom manipulator during path planning, given a cartesian space task path. First, the redundant degree of freedom of the manipulator is represented using arm angle parameterization, and the mapping of joint limits and singular configurations to arm angle space is derived in detail, in conjunction with analytical inverse kinematics solution. Next, based on the cartesian space task path, the arm angle space is discretized to obtain the feasible arm angle range under the self-motion obstacle avoidance condition. The arm angle values determine the joint angles of the manipulator. To minimize task execution time and improve efficiency, the total joint angle displacement of the manipulator is set as the optimization objective, and an improved particle swarm optimization algorithm is employed to iteratively search for the optimal arm angles at each path point. Finally, the effectiveness of the proposed method is validated through both simulation and real machine experiments.

Under the premise of ensuring the safety of the primary task, the proper utilization of the null space of redundant robots can significantly improve human-robot collaboration efficiency, such as in medical surgery or industrial assembly cases. However, the uncertainty of the operation could potentially precipitate unsafe robotic behavior. To guarantee the overall safety of the system, an energy-aware impedance control scheme with safety null space compliance is proposed. The controller employs Cartesian space stiffness shaping and damping injection to bound the system’s energy and power, ensuring safe interaction behaviors. Redundancy is then exploited to handle human-robot interaction behavior by using the designed null space impedance controller while constraining the range of elbow motion. Furthermore, two separate energy tanks are introduced to bolster passivity, with each tank regulated to varying levels and power flows to adapt to the specific requirements of their respective tasks. Three human-robot collaborative experiments with a Franka Research 3 robot are conducted to demonstrate the effectiveness of the proposed approach in enhancing safety and passivity, showcasing its potential in human-robot collaborative manipulation tasks.

Ensuring tracking precision and compliant interaction is essential for robotic manipulation. This requires an accurate robot dynamics model and an effective feedback gain adaptation strategy to improve control performance while preventing excessive stiffness under uncertainties. This article proposes a novel control framework that integrates uncertainty-aware Bayesian neural network (BNN) learning with uncertainty-adapted control design. A BNN infers the nominal model error as a probabilistic distribution, where the predictive mean calibrates the nominal model error and the variance quantifies the learning uncertainty. The control law then compensates for the BNN’s predictive mean, and adaptively adjusts the feedback gain based on the predictive variance. Our BNN is computationally efficient for real-time deployment in robotic control systems. The effectiveness and applicability of the proposed method are demonstrated through both simulation studies and real-world experiments on a 7-DoF robot manipulator.

This article presents a model predictive control (MPC) method for humanoid dual-arm robots (DARs) to realize hybrid force-velocity control in the task space. The proposed method, named hybrid force-velocity MPC (HFV-MPC), enables simultaneous tracking of velocity and external force in the task space, as well as internal force regulation. First, a synchronous decoupling model of internal force, external force, and velocity is developed to address the limitations of conventional methods that decouple internal and external forces solely in the end-effector space and fail to meet the independent regulation requirements of external force and velocity in the task space. Furthermore, a generalized velocity model that integrates task-space velocity, external force, and internal force was established, and a HFV-MPC framework is constructed to enhance system robustness and achieve precise dual-arm force–velocity tracking. Subsequently, a comprehensive MPC cost function is designed, incorporating a dual-arm motion coordination coefficient to suppress undesired redundant joint motions and improve whole-body motion stability. In addition, a feedforward-linearized incremental system is derived, where the incremental model and force prediction jointly construct a generalized state-space model for MPC, to balance modeling accuracy and computational efficiency. Finally, the proposed method is validated in terms of effectiveness and robustness through both simulation and physical robotic experiments.